2. Assume that we have a Cobb-Douglas type aggregate production function in the form: Y = WK" L1-r where. W=technology and r is standard share parameter of Cobb-Douglas production function. а. Find Marginal Rate of Technical Substitution (MRTS) between K and L. b. Why does (or does not) technology affects MRTS? Explain. с. Find output per effective labor; capital per effective labor (y=Y/WL and k= K/WLJ. Find elasticity of substitution between K and L. Why does (or does not) the d. result different from the previous question (Question-1)?

2. Assume that we have a Cobb-Douglas type aggregate production function in the form: Y = WK" L1-r where. W=technology and r is standard share parameter of Cobb-Douglas production function. а. Find Marginal Rate of Technical Substitution (MRTS) between K and L. b. Why does (or does not) technology affects MRTS? Explain. с. Find output per effective labor; capital per effective labor (y=Y/WL and k= K/WLJ. Find elasticity of substitution between K and L. Why does (or does not) the d. result different from the previous question (Question-1)?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter11: Profit Maximization

Section: Chapter Questions

Problem 11.14P

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Assume that we have a Cobb-Douglas type aggregate production function in the form: Y=W.Kr.L1-r where : W=technology and r is standard share parameter of Cobb-Douglas production function. b. Why does (or does not) technology affects MRTS? Explain. c. Find output per effective labor; capital per effective labor (y=Y/WL and k= K/WL ). d. Find elasticity of substitution between K and L. Why does (or does not) the result different from previous question (Question-1) (Y=Ka.Lb) ? (Question 1: Assume that we have a Cobb-Douglas type aggregate production function in the form: Y=Ka.Lb )
Consider the production function Y = K1/2 N12 a. Compute output when K = 49 and N = 81 %3D b. If both capital and labor double, what happens to output? c. Is this production function characterized by constant returns to scale? Explain. d. Write this production function as a relation between output per worker and capital per worker. e. Let K/N = 4. What is Y/N? Now double K/N to 8. Does Y/N double as a result? f. Does the relation between output per worker and capital per worker exhibit constant returns to scale? g. Is your answer to f. the same as your answer to c.? Why or why not?
1. Assume that a firm has the following production function: q = L0.5K0.6 a. Calculate output when L = 64 K = 32. b. What returns to scale does this production function exhibit? c. Calculate output if technology utilized by the firm increases by 25%. d. Determine, both, the marginal product of labour and capital functions (ignore c.). e. Calculate, both, the marginal product of labour and capital when L = 64, K = 32 and interpret your answers. f. Calculate the marginal rate of technical substitution when L = 64, K = 32 and interpret your answer.
QUESTİON: Assume that we have a Cobb-Douglas type aggregate production function in the form: where : W=technology and r is standard share parameter of Cobb-Douglas production function.a. Find Marginal Rate of Technical Substitution (MRTS) between K and L. b. Why does (or does not) technology affects MRTS? Explain. c. Find output per effective labor; capital per effective labor (y=Y/WL and k= K/WL ). d. Find elasticity of substitution between K and L. Why does (or does not) the result different from the previous question (Question-1)?
Assume that Economyland’s production function is Y = F (K, L) = K 0.5 L 0.5Where Y is output level, K is the amount of capital input, and L is the amount of laborinput. a) What is the per-worker production function, y= f (k) for Economyland? b) Assume that 10 percent of capital depreciates each year and savings rate is 20 percent,find the steady-state level of capital per worker for Economyland. Then find the steady-state levelof income per worker and steady-state level of consumption per worker. c) Is it possible to save too much? Why?
1. Suppose the production function for trucks is given by: q = kl + 612 –13 where q represents the weekly quantity of trucks produced, k represents weekly capital input, and I represents weekly labor input. a. Suppose k = 45; at what level of labor input does this average productivity reach a maximum? How many trucks are produced at that point? b. Again assuming that k = 45, at what level of labor input does the total production reach a maximum? How many trucks are produced at that point?
Assume a Cobb-Douglas production function of the form: 3 What type of returns to scale does this production function exhibit? In this instance, returns to scale equal This production function exhibits q=10L0.28K0.59 (Enter a numeric response using a real number rounded to two decimal places.) OA. increasing returns to scale. OB. constant returns to scale. OC. initially decreasing but then constant returns to scale. O D. decreasing returns to scale. O E. initially constant but then decreasing returns to scale.
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Assume that we have a Cobb-Douglas type aggregate production function in the form: Y=W.Kr.L1-r where : W=technology and r is standard share parameter of Cobb-Douglas production function. a. Find Marginal Rate of Technical Substitution (MRTS) between K and L. b. Why does (or does not) technology affects MRTS? Explain. c. Find output per effective labor; capital per effective labor (y=Y/WL and k= K/WL ). d. Find elasticity of substitution between K and L. Why does (or does not) the result different from previous question (Question-1) (Y=Ka.Lb) ?
Consider the Solow-Swan growth model, with a savings rate, s, a depreciation rate, ô, and a population growth rate, n. The production function is given by Y = AK + BK3/4L1/4 where A and B are positive constants. Note that this production is a mixture of Romer's AK model and the neoclassical Cobb- Douglas production function.
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